Optimal estimation for lower bound of the packing number

Youming Liu and Xinyu Qi

Statistics & Probability Letters, 2022, vol. 186, issue C

Abstract: Lower bound estimation of the packing number plays an important role in matrix denoising. By using the metric entropy of the Grassmannian manifold, Cai, Ma and Wu provide a lower bound estimation of the packing number with the metric based on Frobenius norm, see Cai et al. (2013). In this paper, we extend their result to all metrics based on unitarily invariant norms and then give an example to show the optimality of our estimation. Finally, we discuss a potential application in low-rank matrix denoising.

Keywords: Packing number; Lower bound; Covering number; Unitarily invariant norm; Low-rank matrix denoising (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715222000748
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:186:y:2022:i:c:s0167715222000748

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2022.109487

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().